Spectrum mobility as an essential issue has not been fully investigated in mobile cognitive radio networks (CRNs). In this paper, a novel support vector machine based spectrum mobility prediction (SVM-SMP) scheme is presented considering time-varying and space-varying characteristics simultaneously in mobile CRNs. The mobility of cognitive users (CUs) and the working activities of primary users (PUs) are analyzed in theory. And a joint feature vector extraction (JFVE) method is proposed based on the theoretical analysis. Then spectrum mobility prediction is executed through the classification of SVM with a fast convergence speed. Numerical results validate that SVM-SMP gains better short-time prediction accuracy rate and miss prediction rate performance than the two algorithms just depending on the location and speed information. Additionally, a rational parameter design can remedy the prediction performance degradation caused by high speed SUs with strong randomness movements.